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          RL Summary 2-Basic Concept
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      <time title="创建时间：2022-02-12 10:53:40 / 修改时间：12:25:25" itemprop="dateCreated datePublished" datetime="2022-02-12T10:53:40+08:00">2022-02-12</time>
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        <h1 id="专业术语"><a href="#专业术语" class="headerlink" title="专业术语"></a>专业术语</h1><table>
<thead>
<tr>
<th align="center"><strong>名词</strong></th>
<th align="center">Agent</th>
<th align="center">Environment</th>
<th align="center">State</th>
<th align="center">Action</th>
</tr>
</thead>
<tbody><tr>
<td align="center"><strong>解释</strong></td>
<td align="center">行动的主体</td>
<td align="center">主体所在的环境</td>
<td align="center">主体与所处环境的状态 s</td>
<td align="center">主体做出的行为 a</td>
</tr>
<tr>
<td align="center"><strong>名词</strong></td>
<td align="center"><strong>Reward</strong></td>
<td align="center"><strong>Policy</strong></td>
<td align="center"><strong>State transition</strong></td>
<td align="center"></td>
</tr>
<tr>
<td align="center"><strong>解释</strong></td>
<td align="center">回报 r</td>
<td align="center">主体根据回报做出动作所遵循的规则  π(a|s)</td>
<td align="center">状态转换，知道当前状态和行为，预测下一个状态 p(s^|s,a)</td>
<td align="center"></td>
</tr>
</tbody></table>
<ul>
<li>Policy的作用是从包含所有action的集合中抽样，取出Agent要做的action。</li>
<li>状态转移是随机的，因为环境是随机的，而玩家对环境并无全面了解。</li>
<li>强化学习的随机性来自于<strong>行为</strong>和<strong>状态转移</strong>。<strong>行为</strong>是由policy抽样得到的，具有随机性。状态转移随机性见上一条。</li>
</ul>
<h1 id="Return-and-Value"><a href="#Return-and-Value" class="headerlink" title="Return and Value"></a>Return and Value</h1><ul>
<li><p>Return是回报，是所有的奖励之和，它的随机性来自于对未来的不确定。回报用U表示：<br>$$<br>U_t&#x3D;R_t+\gamma R_{t+1}+\gamma^2R_{t+2}+…<br>$$</p>
</li>
<li><p>Action-value function是行动价值函数，它是针对Ut求期望，它能在知道当前状态和行为时，根据policy函数告诉我们当前动作是好是坏。它用Q表示：<br>$$<br>Q_\pi(s_t,a_t)&#x3D;E[U_t|s_t,a_t]<br>$$</p>
</li>
<li><p>Optimal action-value function是最大行动价值函数，它把行动价值函数中的policy函数消掉了。它告诉我们，不管你使用怎样的policy，根据t时刻的状态和行为，你最多能得到多少回报。它的表示如下<br>$$<br>Q^*(s_t,a_t)&#x3D;max_\pi Q_\pi(s_t,a_t)<br>$$</p>
</li>
<li><p>State-value function是状态价值函数，它针对行动价值函数求期望，把A消掉了。它能根据当前状态告诉你场上的局势，例如在围棋中，它能告诉你，你是快赢了还是快输了。它的表示如下<br>$$<br>V_\pi(s_t)&#x3D;E_A[Q_\pi(s_t,A)]<br>$$</p>
</li>
</ul>
<h1 id="强化学习在干什么"><a href="#强化学习在干什么" class="headerlink" title="强化学习在干什么"></a>强化学习在干什么</h1><p>一个简单的循环为：第t个状态下—-&gt;Agent做动作—-&gt;环境更新为第t+1个状态，给Agent第t个奖励，直到游戏结束。</p>
<p>强化学习就是学习policy或者Optimal action-value function，有两者中的一个，就能控制agent。</p>

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